Method of matching, biometric matching apparatus, and computer program

ABSTRACT

A method of matching fingerprints is disclosed. The method comprises, for a first minutia point, being assigned as a planet minutia point a) determining pairs including the planet minutia point and a satellite minutia point, respectively, such that a cluster is formed; b) comparing the clusters of the respective sets and excluding nonmatching satellites; c) counting links in the cluster formed by remaining pairs; and d) for remaining satellite minutia points, performing steps a) to c) with respective satellite minutia point assigned as planet minutia point to form a supercluster by iterating steps a) to d) and superadding the clusters; calculating a score of the supercluster based on the aggregate counted links; and comparing the score with a threshold. A biometric matching apparatus, a portable data carrier, a data processing unit comprising a matching apparatus and a computer program for implementing the invention are also disclosed.

TECHNICAL FIELD

The present invention generally relates to a method of matchingfingerprints to determine if two sets of minutia points of respectivefingerprint reading emanates from fingers which are idem, a biometricmatching apparatus, a portable data carrier, a data processing unitcomprising a matching apparatus, and a computer program.

BACKGROUND

Fingerprint recognition is a growing market hence the need for anongoing development of increasing the performance as well as reducingthe computational complexity in order to achieve efficient matchalgorithms. By using the minutia points as a characterization of afingerprint and follow the current standards in how minutia points aredefined, e.g. International STANDARD ISO/IEC 19794-2 InformationTechnology, Biometric data interchange formats Part 2: Finger Minutiaedata, (2005), fingerprint matching technology has taken a further steptowards mass-market solutions.

Matching two sets of minutia points straight ahead, point by point, is avery difficult task since there is almost always some kind of rotationand/or translation between the sets. This is because the placement ofthe finger on the sensor is usually not on the exact same position as itmight have altered translation or rotation wise. I order to overcomethis problem, some kind of alignment procedure could be performed wheree.g. a verification set is de-translated and/or de-rotated to be in asimilar position as an enrollment set. Once the two sets of minutiapoints are aligned, the individual minutia points could for example bematched all against all to decide which minutia points match between thetwo sets. Finally a metric could be calculated based on how many and howwell the minutia points actually match. The pre-processing of the data,i.e. de-rotating and de-translating, adds requirements on computationaleffort. Simultaneously, user demands put swiftness high ranked, which iscounteracted by the additional processing.

Isenor et al, “Fingerprint matching using graph matching”, University ofToronto, discloses an approach where a fingerprint is encoded in form ofa graph, in which nodes represent ridges and edges represent ridgeadjacency information. A directed graph is thus defined, where each nodein the graph corresponds to one ridge. Edges between nodes are labeledbased on the nodes they interconnect. The graphs are partitioned,refined and thereafter scored by tracing a tree in each graph.

WO 96/12246 A1 discloses an image comparison arrangement wherefingerprint minutia maps are converted to attributed relation graphs,ARG, including nodes and branches. In the ARG, a comparison tree bywhich attempts are made to fill a match core with elements representingmatching stars. The number of elements in the match core indicates thedegree of match.

EP 2237226 A1 discloses an approach for inter-pattern featurecorrespondence relationships. A proximity feature point group isgenerated in which feature points are positionally proximate to eachother in a pattern and a location relationship number numeric groupindicating location relationship between the feature points. The featurepoint related arrangement relationships numerical value used formatching check of the feature point group arrangements is measured byusing a general image coordinate system for a reference coordinatesystem. A score is derived from the number of corresponding featurepoints.

GB 2050026 A discloses an approach where minutiae of a fingerprint arecombined with counts and density for each feature point selected as areference feature point. The density is determined in connection withadjacent feature points that are present in a predeterminedneighbourhood of the reference feature point. Each count is decided bynumber of streaks intervening between the reference feature point amongthe feature points in a predetermined sector of the neighbourhood.

The solutions presented above still are complex and/or resourceconsuming. It is therefore a desire to provide an improved approach ofbiometric matching of sets of minutiae.

SUMMARY

An object of the invention is to at least alleviate the above statedproblem. The present invention is based on the understanding that aconvenient and reliable metric, with smooth granularity, can be achievedby matching pairs of minutia points and building a structure therefromin which the metric is achieved as the structure is built.

According to a first aspect, there is provided a method of matchingfingerprints to determine if two sets of minutia points of respectivefingerprint reading emanates from fingers which are idem. The methodcomprises, for a first minutia point in respective set being assigned asa planet minutia point, a) determining pairs including the planetminutia point and a satellite minutia point, respectively, such that acluster is formed around the first minutia point in the respective setwith the satellite minutia points; b) comparing the clusters of therespective sets which have matching features of the pairs between thesets and excluding non-matching satellites; and c) counting links in thecluster formed by remaining pairs of the planet minutia point and thesatellite minutia points. For remaining satellite minutia points,performing a) determining pairs including the planet minutia point and asatellite minutia point, respectively, such that a cluster is formedaround the first minutia point in the respective set with the satelliteminutia points; b) comparing the clusters of the respective sets whichhave matching features of the pairs between the sets and excludingnon-matching satellites; and c) counting links in the cluster formed byremaining pairs of the planet minutia point and the satellite minutiapoints with respective satellite minutia point assigned as planetminutia point to form a supercluster. This is iterated and superaddingof the clusters of each iteration is performed wherein link count isstored such that an aggregate link count is available after theiteration such that the aggregate link count is achieved as thesupercluster is built. The method further comprises calculating a scoreof the supercluster based on the aggregate counted links; and comparingthe score with a threshold, wherein the respective fingerprint readingsare considered to emanate from fingers which are idem if the scorereaches the threshold.

For remaining satellites, the process may include performing theiterative steps until the formed supercluster reaches a predeterminedsize or no further minutia points of the sets remain.

The matching features of the pairs may comprise a set of parametersincluding any of distance between planet minutia point and satelliteminutia point; relative angle between planet minutia point and satelliteminutia point; and relative angle between a reference angle and an angleof any of the planet minutia point and satellite minutia point, or anycombination of these.

The calculation of the score may further comprise calculating a tensionparameter of the supercluster and basing the score on the calculatedtension parameter.

The calculation of the score may further comprise calculating an area ofthe supercluster and basing the score on the calculated area.

The calculation of the score may further comprise calculating a meannumber of minutia points in the sets and basing the score on thecalculated mean number of minutia points.

The calculation of the score may further comprise calculating the numberof minutia points in the supercluster and basing the score on thecalculated number of minutia.

The score may be calculated as a quota comprising in its numerator aproduct comprising the number of counted links, the tension parameterand the area of the supercluster, and in its denominator a productcomprising the squared mean number of minutia points in the sets and thesquared number of minutia points in the supercluster.

The initial planet may be selected close to a centre of the fingerprintreading. The initial planet may additionally or alternatively beselected such that a first cluster comprises as many matching pairs aspossible, wherein the method further comprises repeating the firstiteration with another planet if a poor match is given for a previousselected initial planet.

According to a second aspect, there is provided a biometric matchingapparatus comprising a receiver for receiving a first set of minutiapoints of a fingerprint reading; a memory access circuit arranged toaccess a memory holding at least a second set of minutia points of afingerprint template; and a processing device connected to the receiverand the memory access circuit, and arranged to determine whether thefirst set of minutia points match the second set of minutia points. Thisis performed by, for a first minutia point in respective set, beingassigned as a planet minutia point a) determine pairs including theplanet minutia point and a satellite minutia point, respectively, suchthat a cluster is formed around the first minutia point in therespective set with the satellite minutia points; b) compare theclusters of the respective sets which have matching features of thepairs between the sets and excluding non-matching satellites; c) countlinks in the cluster formed by remaining pairs of the planet minutiapoint and the satellite minutia points; and d) for remaining satelliteminutia points, perform a) to c) with respective satellite minutia pointassigned as planet minutia point to form a supercluster by iteration ofsteps a) to d) and superaddition of the clusters of each iterationwherein link count is stored such that an aggregate link count isavailable after the iteration such that the aggregate link count isachieved as the supercluster is built; calculate a score of thesupercluster based on the aggregate counted links; and compare the scorewith a threshold, wherein the respective fingerprint reading andtemplate are considered to emanate from fingers which are idem if thescore reaches the threshold, such that an output indicating whether thefingerprint reading and template match is provided.

The matching features of the pairs may comprises a set of parametersincluding any of distance between planet minutia point and satelliteminutia point; relative angle between planet minutia point and satelliteminutia point; and relative angle between a reference angle and an angleof any of the planet minutia point and satellite minutia point, or anycombination of these.

For the calculation of the score, the processing device may further bearranged to calculate a tension parameter of the supercluster and basethe score on the calculated tension parameter.

For the calculation of the score, the processing device may further bearranged to calculate an area of the supercluster and base the score onthe calculated area.

For the calculation of the score, the processing device may further bearranged to calculate a mean number of minutia points in the sets andbase the score on the calculated mean number of minutia points.

For the calculation of the score, the processing device may further bearranged to calculate the number of minutia points in the superclusterand base the score on the calculated number of minutia.

The score may be calculated as a quota comprising in its numerator aproduct comprising the number of counted links, the tension parameterand the area of the supercluster, and in its denominator a productcomprising the squared mean number of minutia points in the sets and thesquared number of minutia points in the supercluster.

The initial planet may be selected close to a centre of the fingerprintreading. Alternatively or additionally, the initial planet may beselected such that a first cluster comprises as many matching pairs aspossible, wherein the processing device is arranged to repeat the firstiteration with another planet if a poor match is given for a previousselected initial planet.

According to a third aspect, there is provided a portable data carriercomprising a memory holding a template of a fingerprint represented by aset of minutia points of a reference fingerprint; a matching apparatusaccording to the second aspect, wherein the memory access means isconnected to the memory, arranged to determine if the first set ofminutia points and the set of minutia points of a reference fingerprintemanates from idem finger; and a security mechanism arranged to beunlocked upon the output indicating that the fingerprint reading andtemplate match.

According to a fourth aspect, there is provided a data processing unitcomprising a matching apparatus according to the second aspect, whereinthe accessed memory is a database comprising a plurality of templatesfor a plurality of fingers, respectively, arranged to determine, from acalculated score for respective of the templates, which of templatesthat resembles the fingerprint to be checked the most.

The data processing unit may further be arranged to determine if thefingerprint to be checked and the most resembling one of the at leastone template emanates from fingers which are idem by comparing the scoreof the most resembling one of the at least one template with athreshold.

According to a fifth aspect, there is provided a computer programcomprising computer executable instructions, which instructions cause acomputer to, when downloaded to and executed on a processor of thecomputer, perform the method according to the first aspect. Otherobjectives, features and advantages of the present invention will appearfrom the following detailed disclosure, from the attached dependentclaims as well as from the drawings. Generally, all terms used in theclaims are to be interpreted according to their ordinary meaning in thetechnical field, unless explicitly defined otherwise herein. Allreferences to “a/an/the [element, device, component, means, step, etc]”are to be interpreted openly as referring to at least one instance ofsaid element, device, component, means, step, etc., unless explicitlystated otherwise. The steps of any method disclosed herein do not haveto be performed in the exact order disclosed, unless explicitly stated.

BRIEF DESCRIPTION OF THE DRAWINGS

The above, as well as additional objects, features and advantages of thepresent invention, will be better understood through the followingillustrative and non-limiting detailed description of preferredembodiments of the present invention, with reference to the appendeddrawings.

FIG. 1 illustrates an exemplary fingerprint image and exemplary minutiaefound in it.

FIG. 2 illustrates a minutiae pair and parameters derivable from it.

FIG. 3 illustrates a minutiae pair and exemplary tolerances for theparameters when matching with a corresponding minutiae pair.

FIG. 4 illustrates two sets of minutiae that are to be compared, andinitially building a cluster by forming matching pairs.

FIG. 5 illustrates the two sets of minutiae upon continuing building asupercluster by superaddition of cluster formed by further matchingpairs.

FIG. 6 illustrates the two sets of minutiae when the supercluster isbuilt.

FIG. 7 illustrates the built supercluster per se.

FIG. 8 is a flow chart illustrating a method.

FIG. 9 is a block diagram schematically illustrating an apparatus.

FIG. 10 illustrates a comparison between two formed superclusters, andtheir similarities and differences in sense of observed metrics.

FIG. 11 illustrates a non-transitory computer-readable medium and aprocessing means.

FIG. 12 illustrates two sets of minutiae that are to be compared, inwhich a systematic error of general direction of the pairs r isdetermined.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

For the understanding of fingerprint representation and matching, whichis the basis for the present invention, some basic facts will be givenbelow, and the concept of the invention will be described by introducingfeatures stepwise for the better understanding of the particulars of theinvention, and also the invention as a whole. The effect of respectivefeature, as well as the effect of the invention as a whole, may becomemore clear taking the whole disclosure into consideration.

FIG. 1 illustrates an exemplary fingerprint image to the left andexemplary minutiae found in it, which are separately illustrated to theright. A minutia point can be assigned a parameter set for describingit. The parameter set can comprise the position of the minutia point,here illustrated as the position of the respective circles, e.g. in acoordinate system having its reference to the sensor, or to a referencepoint determined from the image. The parameter set can also comprise adirection of the minutia, here illustrated as a line in a direction fromthe respective circles, a type of the minutia, etc. These parameters areknown in the art. For speeding up comparison, and/or enabling comparisonon devices with limited processing power and/or memory capacity, theparameters used in a biometric application can be limited to a sub-setof these parameters. In the example illustrated in FIG. 2 belowindicates a way of reducing the parameter set while maintaining anefficient and reliable representation of features of the fingerprint. InFIGS. 2 and 3, the line illustrating the direction from the circle isenhanced with an arrow to more easily discriminate it from other linesused in the illustration.

Matching two sets of minutia points directly, point by point, causessome problems since there is almost always some kind of rotation and/ortranslation between a verification set of minutiae with respect to anenrolment set of minutiae. This is because the placement of the fingeron a sensor is usually not on the exact same position, and the image hasaltered by translation and/or rotation. I order to overcome this problemsome kind of alignment procedure could be performed where theverification set is de-translated and/or de-rotated to be in a similarposition as the enrolment set. Once the two sets of minutia points arealigned, the individual minutia points could for example be matched allagainst all to decide which minutia points match between the two sets.From this, a score could be calculated based on how many and how wellthe minutia points actually match. However, the present inventionsuggests another approach. The inventive approach is based on that onlya relative comparison is done where local structures formed from theenrolment set are compared to local structures formed from theverification set. If these local structures are translation and rotationinvariant, no specific alignment step is needed. The simplest localstructure, which is translation and rotation invariant, is a pair ofminutia points, located not too far apart but not too closely spacedeither.

FIG. 2 illustrates a minutiae pair and parameters derivable from it. Byusing two minutia points, parameters of the points can be determinedfrom a relative reference, wherein alignment in sense of translation androtation will be included in the determination of the pair, and may notneed involving any external reference point or coordinate system. In theillustrated minutiae pair, a reference for direction α for the firstminutia, direction β for the second minutia and angle θ for the areused, here to the horizontal plane, while a distance d between thepoints is entirely relative. As an alternative, the direction α for thefirst minutia and direction β for the second minutia may be representedas relative to a line between the points, and then becomes relative,while the angle θ will be to a reference direction. However, uponcomparison between two representations including such pairs, the angle θwill be different for the comparison sets due to different rotation, andcan be excluded by a relative value between the sets. The localstructures then become translation and rotation invariant relative toeach other. Further, the granularity with which the parameters arerepresented, preferably digitally represented, may vary depending on thebiometric application. Also here, the issue of speeding up comparison,and/or enabling comparison on devices with limited processing powerand/or memory capacity may be considered. For example, the directionsmay be quantised into 16, 32, 64, etc. directions for representing thecomplete turn by 4, 5, 6, etc. bits. Normally, even if hardware soallows, accuracy is not very much increased by using more than 8 bitsfor a direction parameter, wherein 8 bits can be seen as a preferredvalue if the hardware so allows.

These types of pairs form the basic building block used in the followingdisclosure. It could be mentioned that most alignment algorithms usedsome kind of local structures to calculate the translation and rotationdifference between the two sets of minutia points but in the followingdisclosure, the matching is performed accordingly.

FIG. 3 illustrates a minutiae pair and exemplary tolerances for theparameters when matching with corresponding minutiae pair. To provide anefficient matching, a certain tolerance enables issues such asquantisation errors, deformation of finger when applying it to sensorand imperfections in sensors to be handled. In FIG. 3, the sameparameter set as illustrated in FIG. 2 has been selected for the sake ofeasier understanding, but as demonstrated above with reference to FIG.2, the parameters can be defined in other ways. The angle α, whencomparing with the other set, will be considered equal if the comparedminutia has its direction within the range Δα. Similarly, the angle β,when comparing with the other set, will be considered equal if thecompared minutia has its direction within the range Δβ, and the angle θ,when comparing with the other set, will be considered equal if thecompared pair has its direction within the range Δθ. Also similarly, thedistance d, when comparing with the other set, will be considered equalif the compared pair has its distance within the range Δd.

The deviation parameters Δd, Δα, Δβ and Δθ are mainly used for givingunderstanding of the principles. The tolerances are of course notnecessary to be determined by any such deviation parameters. An exampleis to observe a differential value between respective pair, i.e. tosubtract one parameter from the other and compare the absolute value ofthe subtraction with a threshold value chosen to give an appropriatetolerance. Such operations are particularly suitable for quickcalculations by logic circuitry. Furthermore, to make comparison moreinvariant to alignment issues, differential values of both the generaldirections of the minutia points of respective pair can be derived insimilar way. For example, the following calculations and checks tothreshold values can be made

|d _(s) −d _(t) |<T _(d)

|(β_(s)−α_(s))−(β_(t)−α_(t))|<T _(αβ)

|(β_(s)−θ_(s))−(β_(t)−θ_(t))|<T _(βθ)

where d_(s) is distance of the sample pair, d_(t) is distance of thetemplate pair, T_(d) is a chosen threshold giving appropriate tolerancein distance, β_(s) is general direction of one minutia point of thesample pair and α_(s) is general direction of the other minutia point ofthe sample pair, β_(t) is general direction of one minutia point of thetemplate pair and α_(t) is general direction of the other minutia pointof the template pair, T_(αβ) is a chosen threshold giving appropriatetolerance in differential value between general directions of theminutia points, θ_(s) is a direction between minutia points of thesample pair, θ_(t) a direction between minutia points of the templatepair, and T_(βθ) is a chosen threshold giving appropriate tolerance indifferential value between one of the general directions of the minutiapoints and a reference direction. In this example, suitable thresholdshave been a value corresponding to about a few tenths of a mm for T_(d),about a few tenths of a radian for T_(αβ), and about a few tenths of aradian for T_(βθ). These values are preferably fine-tuned for thespecific application, used gear, and quantisation used by the logiccircuitry. According to an embodiment, the threshold for T_(d) can betuned to a value somewhere between 0.5 and 1.0 mm, to a value somewherebetween 0.4 and 0.8 radians for T_(αβ), and to a value somewhere between0.4 and 0.8 radians for T_(βθ). According to a further embodiment, thethreshold for T_(d) can be tuned to a value somewhere between 0.2 and0.7 mm, to a value somewhere between 0.4 and 0.8 radians for T_(αβ), andto a value somewhere between 0.2 and 0.5 radians for T_(βθ). Accordingto a further embodiment, the threshold for T_(d) can be tuned to a valuesomewhere between 0.3 and 0.6 mm, to a value somewhere between 0.1 and0.4 radians for T_(αβ), and to a value somewhere between 0.2 and 0.5radians for T_(βθ). According to a further embodiment, the threshold forT_(d) can be tuned to a value somewhere between 0.2 and 0.5 mm, to avalue somewhere between 0.2 and 0.6 radians for T_(αβ), and to a valuesomewhere between 0.3 and 0.8 radians for T_(βθ). According to a furtherembodiment, the threshold for T_(d) can be tuned to a value somewherebetween 0.2 and 0.5 mm, to a value somewhere between 0.2 and 0.5 radiansfor T_(αβ), and to a value somewhere between 0.2 and 0.5 radians forT_(βθ). According to a further embodiment, where tight tolerances arepreferred, the threshold for T_(d) can be tuned to 0.1 mm, to a value ofabout 0.1 radian for T_(αβ), and to a value of about 0.1 radians forT_(βθ). According to a further embodiment, where tolerances which likelyavoid missing a match are preferred, the threshold for T_(d) can betuned to about 1 mm, to a value of about 1 radian for T_(αβ), and to avalue of about 1 radians for T_(βθ).

FIG. 4 illustrates two sets of minutiae that are to be compared, andinitially building a cluster by forming matching pairs. In theillustration, the star-shaped symbols denote representations ofminutiae, where position and orientation is indicated. Further, thefive-pointed star symbol denotes a selected planet minutia point and thefour-pointed star symbols denote its possible satellite minutia points.The left-hand set can be considered as the minutiae representation of asample and the right-hand set can be considered as the minutiaerepresentation of a template, which sample is to be compared with thetemplate for determining whether a match is present. From the planetminutia point pairs are formed with respective satellite minutia point,as illustrated by respective lines between the planet and satelliteminutia points, and the pairs are compared between the sample and thetemplate according to the principles demonstrated with reference toFIGS. 2 and 3. The matching features of the pairs preferably comprises aset of parameters including any of distance between planet minutia pointand satellite minutia point, relative angle between planet minutia pointand satellite minutia point, and relative angle between a referenceangle and an angle of any of the planet minutia point and satelliteminutia point, or any combination of these.

Upon the selection of pairs of planet minutia point and satelliteminutia point, it is preferred that only pairs having an upper and/or alower bound in sense of distance between the planet minutia point andsatellite minutia point. Choosing pairs having very short distance maycause problems in sense of for example large relative quantisation errorof the distance parameter and/or large deviation in angle parameter(s).Choosing pairs having very long distance may cause problems in sense offor example error of the distance parameter and/or angle parameter(s)due to deformation of fingerprint at reading due to different pressureor tension against reading device, and/or causing the cluster to beinappropriate for comparison. Therefore, the upper and lower bounds arepreferably set to appropriate support the implementation in sense ofsensor size, resolution, quantization, etc.

Further, the solid lines indicate pairs where a match is found and thedashed lines indicate pairs where no match is found. In this example,five matching pairs are found, and these can consequently be seen bothin the sample and the template illustration. These matching pairs formfive links in the cluster and consequently the first five links in asupercluster to be built. It can also be observed that the pair with thelowermost minutia point did not match due to position and orientationalthough seeming close to hit, which may be a typical phenomenon ofdeformation upon acquiring the sample. Below, with reference to FIG. 6,it is indicated that this minutia point is involved with a match in apair with another minutia point, which is possible when the relativedeformation between those minutia points is less. This is one examplewhere the link count gives a reasonable metric, i.e. the count is lessthan if no deformation occurred, but gives a contribution to the metricanyway to some, often close-by, minutia points forming matching pairs,and the resolution in the matching score of the supercluster isimproved. An aspect of providing a score is further elucidated withreference to FIG. 10 below.

Upon selecting the first planet, one or a few criteria can be set. Sinceit is desirable to be able to build a supercluster that covers as muchas possible of the minutiae of the fingerprint, choosing a planet fromwhich only an isolated supercluster can be built should be avoided. Thisis of course hard to predict before the supercluster is built, but aninception can be to choose the first planet close to the centre of theimage and/or a planet that provides a first matching cluster providingas many matching pairs as possible. The latter can imply that the firstcluster is re-made with another planet if the first one gives a poormatch. If several attempts give no or few matching pairs, the case canbe that the fingerprints are not matching, and that can be output as aresult directly without spending a lot of processing on building a poorsupercluster that would clearly give a score that would not reach thethreshold of match anyway. If the mismatch was due to a bad reading ofthe sample fingerprint, the user will then be able to make a new readingfaster if a quick fail result can be provided.

Further, the cluster of the sample is compared to a plurality ofpossible clusters of the template since difference in translationbetween the sample and template may be unknown. A likely cluster, i.e.providing enough of matching pairs, at a coarse initial matching, e.g.only based on general directions of pairs and possibly with an increasedtolerance, can be selected for a more thorough comparison according towhat has been demonstrated above. Alternatively, parallel inceptioncomparisons can be made, where progress in matching for respectiveinception is evaluated, and lack of matching causes some of the parallelcomparisons to stop, and finally only one, if there seems to be anymatch, remains and will form the first cluster. In addition to any ofthe alternatives above, a systematic error in general direction of thepairs can be taken into account as the processes progress to form arotation calibrated comparison. In such case, instead of comparing forexample |θ_(s)−θ_(t)|<Δθ, a comparison can comprise |θ_(s)−θ_(t)+r|<Δθ,where θ_(s) is angle of sample pair, θ_(t) is angle of template pair, Δθis tolerance in angle for match, and r is determined systematic error ingeneral direction of the pairs, i.e. rotation between sample andtemplate, as is schematically illustrated for a pair in FIG. 12. Theparameter r can for example be determined from one or several found goodmatches, and can help to enhance comparison further on in the process.In FIG. 12, a good match is illustrated between the minutia sets to becompared, but the error in general direction r is determined. This isillustrated by the general direction of the left set being illustratedalso, as indicated by the arced arrow, in the right set as a dottedline. The angle between the dotted line and the general direction foundin the right set, illustrated by a solid line, becomes an estimate ofthe error in general direction r. The illustration is schematic, and inpractise the error in general direction r is preferably estimated from aplurality of good matches, e.g. by statistical analysis such asaveraging or weighted averaging. Here, the weighting can be made basedon metrics on the quality of the match for respective pair, i.e.difference in value of compared parameters.

For the comparisons, which can be numerous, the parameters to becompared for respective pairs are preferably calculated once and thenstored in matrix form, which then is quickly accessed for eachcomparison.

FIG. 5 illustrates the two sets of minutiae in the next iteration, whereanother of the minutia points is selected as planet minutia point. Thenotation is the same as for FIG. 4. In the example, six matching pairsare found, and these can consequently be seen both in the sample and thetemplate illustration. It is to be observed that one of the matchingpairs were also present in the first matching illustrated in FIG. 4.Here, the decision to count that matching twice or not is a choice ofimplementation. The principle remains the same. These matching pairsform six more links, or five if implemented not to count the same matchtwice, in the cluster and consequently the eleven (or ten) links aresuperadded in the supercluster to be built.

When a satellite is chosen as the new planet, the comparison is somewhatdifferent from the initial comparison, where all clusters of thetemplate was considered. Instead, when a satellite is chosen as the newplanet, comparison is only made with the cluster from the correspondingminutiae point of the template. This will make the process faster whencontinuing to build the supercluster.

The procedure is iterated such that all of the minutia points, or atleast all minutia points that have been a matching satellite minutiapoint to another planet minutia point, have been considered as a planetminutia point, or the formed supercluster reaches a predetermined size,and each found matching pair, i.e. formed link, is counted according tothe principles elucidated above. This is illustrated in FIG. 6 as thebuilt supercluster. In FIG. 6, the mutual matching pairs, i.e. where thelinks are present twice, are not illustrated for clarity reasons.

It is to be noted that there may be more than one supercluster in forexample the sample. The reason for this can for example be that a partof the sample contain so much noise for example in a part that onecontinuous supercluster is not able to be formed. Another example wheresuch issues can arise is when a so called swipe sensor, i.e. a sensorwhich the finger is swiped over such that a plurality of images areacquired from which the minutiae are extracted, is used and some of theacquired images lack recognisable minutiae. In such case, there is anoption that for example two superclusters are formed, and their relationto each other, e.g. by angle and/or distance/direction, make themcorrespond to parts of the supercluster of the template. In such case,aggregate score can be calculated from the two or more superclusters,and that can still be enough for reaching the matching threshold.

FIG. 7 illustrates an example of a created supercluster. It should benoted that for the sake of easier understanding, the illustratedsupercluster is made from a limited set of minutia points. In practice,the number of minutia points included for generating the supercluster ispreferably also limited due to trade-off between performance in sense ofachieving a reliable result and performance in sense of processing timeand available processing power and/or power consumption. The limitationcan be achieved, when having a large amount of minutia points availableboth in the template and in the sample, by building the superclusteruntil a desired size is achieved, or by limiting the amount of minutiapoints in the template and/or the sample before commencing the matching.For example, the number of minutia points of the supercluster can belimited to about 64 by any of the approaches demonstrated above, whichhas proven to give a good trade-off in performance.

FIG. 7 represents the supercluster only by its links, since theinformation about the respective minutia points of the sample andtemplate sets no longer is needed for the determination whether there isa match or not between the sample and the template. From the builtsupercluster link configuration, a decision whether the sample and thetemplate match can be taken. The decision is basically taken on a scorebased on the aggregate number of links, which is compared to a scorethreshold. For further enhancing the score calculation, further aspectsof the supercluster can be considered. For example, the calculation ofthe score further comprises calculating a tension parameter of thesupercluster and basing the score also on the calculated tensionparameter, where tension here means the size of an array forrepresenting the supercluster. Here, the meaning of “further comprise”,as also below, be seen as “in addition to the link count”, which is thebasis for score calculation in all the given examples. The calculationof the score can also, or alternatively, further comprise calculating anarea of the supercluster and basing the score on the calculated area.Here, the area of the supercluster can be calculated as a minimumrectangle to enclose the supercluster, i.e. min/max x/y for extremes ofminutia points included in supercluster. Alternatively, the area can becalculated as a true area of the supercluster, which however becomes amore complex calculation operation. Still further, the calculation ofthe score can also, or alternatively, further comprise calculating amean number of minutia points in the sets and basing the score on thecalculated mean number of minutia points, which means that larger setsare given a different score than smaller sets. This can be combined orreplaced by calculating the number of minutia points in the superclusterand basing the score on the calculated number of minutia. The combinedcalculation can include forming a ratio between the number of minutiapoints of the built supercluster and the number of minutia points of thesets, where the number of minutia points can be the number of minutiapoints of the sample, of the template, or a mean or sum of the number ofminutia points of the sample and template. The way of actually countingthe score is preferably decided based on the implementation. Forexample, the score is calculated as a quota comprising in its numeratora product comprising the number of counted links, the tension parameterand the area of the supercluster, and in its denominator a productcomprising the squared mean number of minutia points in the sets and thesquared number of minutia points in the supercluster. This example hasbeen found to give a proper balance between the different parameterswhich is suitable also to high-end solutions where performance both insense of reliability, such as false rejection rate and false acceptancerate, and in sense of computing effort on scarce resources, i.e. toprovide fast processing also on e.g. portable devices.

FIG. 8 is a flow chart illustrating a method of matching fingerprintsaccording to an embodiment. In a minutia point set collection step 100,a minutia point set to be compared is collected, and at least one otherminutia point set is also collected to be compared with. Here, one otherminutia point set is collected when a pure matching is to be performed,e.g. for authenticating a user, and a plurality of other minutia pointsets are collected when an identification is to be performed in additionto the matching. The term collecting can mean different things dependingto the implementation. For the minutia point set to be compared, thecollecting can comprise reading a fingerprint image from a sensor andextracting the minutia point set from the acquired image. Thefingerprint image can be presented from another entity or context, wherethe collecting comprises receiving or accessing the fingerprint imageand extracting the minutia point set from it. Further, the minutia pointset can be presented from another entity or context, where thecollecting comprises receiving or accessing the minutia point set,hereafter called the sample. Similar, for the other minutia point set orsets, hereafter called the template, the information is received oraccessed from e.g. a server, memory or data carrier. It is to be noted,for the case a plurality of templates are in question, the steps until ascore is calculated can be considered as parallel processes for eachtemplate. Here, the processes can be aborted in the course of time whenlink counting scores, as will be elucidated below, do not growsatisfactory to save processing power. An identified and matchingtemplate can be determined in the end after scores are determined,respectively.

The process will now be described as a matching of a sample to atemplate, but it should be understood that the principle of one sampleto many templates follows the same approach, as indicated above.

In a pair determination step 101, pairs are determined from a determinedplanet minutia point to other minutia points being satellite minutiapoints, as demonstrated with reference to FIGS. 2 to 7. A clusteremanating from this planet minutia point is thus formed for respectiveset of minutia, i.e. for the sample and the template. In a comparisonstep 102, the respective pairs of the clusters of the respective setsare then compared, similar to what is demonstrated with reference toFIG. 3. Non-matching satellites are excluded from the cluster inexclusion step 103, and the remaining pairs, i.e. the links, are countedin a link counting step 104. The link count is stored such that anaggregate link count is available after proper iterations. A new minutiapoint is then set to be the planet minutia point in step 105, and unlessa supercluster is considered to be ready in a supercluster finishedchecking step 106, based on any criterion as of those demonstrated abovewith reference to FIG. 7, the procedure returns to perform steps 101 to104 from the point of view of the new planet minutia point. If thesupercluster is considered ready in step 106, the process continues to ascore calculation step 107, where the aggregate number of link countsplays the dominant role. Other parameters may also be included, asdemonstrated above with reference to FIG. 7. The determined score iscompared with a threshold in match determination step 108, and if thescore exceeds the threshold, a match is considered to be present.

For the case of comparison of a sample with multiple templates, thetemplate for which the sample gains the highest score is compared withthe threshold, and the procedure of matching is performed accordingly.

FIG. 9 schematically illustrates a biometric matching apparatus 200comprising a receiver 201 for receiving a first set of minutia points ofa fingerprint reading, a memory access circuit 202 arranged to access amemory holding at least a second set of minutia points of a fingerprinttemplate, and a processing device 203 connected to the receiver 201 andthe memory access circuit 202, and arranged to determine whether thefirst set of minutia points match the second set of minutia points, andproviding an output, depending on the result, via a transmitter 204.

The receiver 201 should be broadly construed to be a functional elementarranged to collect a set of minutia points representing a biometricsample. The collecting can comprise reading a fingerprint image from asensor and extracting the minutia point set from the acquired image, andin such case the receiver 201 comprises a biometric sensor and anextraction circuit. The biometric sample, e.g. a fingerprint image, canbe presented from another entity or context, where the collectingcomprises receiving or accessing the fingerprint image and extractingthe minutia point set from it, and in such case the receiver 201comprises a communication circuit, for wired or wireless communication,for receiving the image data, and an extractor circuit. Further, theminutia point set can be presented from another entity or context, wherethe collecting comprises receiving or accessing the minutia point set,and in such case the receiver 201 comprises a communication circuit, forwired or wireless communication, for receiving the minutia point data.

The memory access circuit 202 which is arranged to access a memoryholding at least a second set of minutia points of a fingerprinttemplate may be comprised in the processing device 203 or in a memory,and should be functionally construed. The memory can be a server, avolatile memory temporarily storing the one or more templates during thematching, a non-volatile memory, e.g. on a data carrier, forming a partof an identification item, or other data holding equipment suitable forthe implementation in question. In certain cases, the memory may be apart of the processing device 203, which can be particularly suitablewhen template is to be kept secret, and the processing device 203 isenabled to store the template in a secure memory area on its chip. Thiswill make it more or less impossible to tamper or steal the data.

The transmitter 204 should also be functionally construed, and may be apart of the processing device 203, where for example a secret, such asan access, authentication or decryption key, is “transmitted” internallyin the processing device or its peripheral devices to enable a certainfunction upon match.

The processing device 203 can be, depending on the implementation andits purpose, anything from an embedded processor of a smart card to anation or world wide data network, e.g. for financial, intelligence,infrastructural, or other purposes gaining benefit from matching oridentification of biometrics, and there between personal computing orportable communication devices gaining benefit by e.g. replacingpasswords and identification numbers with convenient biometricsolutions.

The biometric matching apparatus 200 is arranged, by its functionalelements 201-204, to implement the functions demonstrated above withreference to FIGS. 2 to 8.

FIG. 10 illustrates two comparable superclusters, each formed from acomparison between a sample and a template, and differences in metricsgained from different approaches of counting scores. Both superclustershave ten found minutia points included in the respective matching pairs.If only the number of minutia points were to be used as a metric on thematching, the two would be equal. However, the left supercluster would,by employing a link count approach, have 32 counted links. It can benoted here, that found pairs are allowed to be counted twice in thisexample when first one minutia point of a pair is considered to beplanet minutia point, and then the other of the pair. The right one havemore matching pairs, and thus 42 links have been counted. The agreementbetween the sample and template were in the right case larger than inthe left case although the same number of matching minutia points wereidentified. From this, it can be seen that a link count approach gives afiner granularity of matching score, which has been found to improvematching and identification.

The methods according to the present invention are suitable forimplementation with aid of processing means, such as computers and/orprocessors. Therefore, there is provided computer programs, comprisinginstructions arranged to cause circuit or circuits of the processingmeans, processor, or computer to perform the steps of any of the methodsaccording to any of the embodiments described with reference to FIG. 8,taken in light of the principles described with reference to FIGS. 2 to7. The computer programs preferably comprises program code which isstored on a computer readable medium 300, which can be non-transitory asillustrated in FIG. 11, and which can be loaded and executed by aprocessing means, processor, or computer 302 to cause circuit orcircuits thereof to perform the methods, respectively, according toembodiments of the present invention, preferably as any of theembodiments described with reference to FIGS. 2 to 8. The computer 302and computer program product 300 can be arranged to execute the programcode sequentially where actions of the any of the methods are performedstepwise. The processing means, processor, or computer 302 is preferablywhat normally is referred to as an embedded system. Thus, the depictedcomputer readable medium 300 and computer 302 in FIG. 11 should beconstrued to be for illustrative purposes only to provide understandingof the principle, and not to be construed as any direct illustration ofthe elements.

The invention has been made in the context of matching fingerprints. Theuse of the principles may equally well be used for other matchingoperations where biometric data, represented as features, i.e. minutiaepoints, and their relation to each other, is to be compared, such as inthe context of finger vein pattern, iris, palm or foot prints, dentalidentification, etc.

The invention has mainly been described above with reference to a fewembodiments. However, as is readily appreciated by a person skilled inthe art, other embodiments than the ones disclosed above are equallypossible within the scope of the invention, as defined by the appendedpatent claims.

1. A method of matching fingerprints to determine if two sets of minutiapoints of respective fingerprint reading emanates from fingers which areidem, the method comprising a processing device performing the steps of:for a first minutia point in respective set, being assigned as a planetminutia point a) determining pairs including the planet minutia pointand a satellite minutia point, respectively, such that a cluster isformed around the first minutia point in the respective set with thesatellite minutia points; b) comparing the clusters of the respectivesets which have matching features of the pairs between the sets andexcluding non-matching satellites; c) counting links in the clusterformed by remaining pairs of the planet minutia point and the satelliteminutia points; and d) for remaining satellite minutia points,performing steps a) to c) with respective satellite minutia pointassigned as planet minutia point to form a supercluster by iteratingsteps a) to d) and superadding the clusters of each iteration whereinlink count is stored such that an aggregate link count is availableafter the iteration such that the aggregate link count is achieved asthe supercluster is built; calculating a score of the supercluster basedon the aggregate counted links; and comparing the score with athreshold, wherein the respective fingerprint readings are considered toemanate from fingers which are idem if the score reaches the threshold.2. The method according to claim 1, wherein, for remaining satellitesafter step d), performing steps a) to d) until the formed superclusterreaches a predetermined size or no further minutia points of the setsremain.
 3. The method according to claim 1, wherein the matchingfeatures of the pairs comprises a set of parameters including any ofdistance between planet minutia point and satellite minutia point;relative angle between planet minutia point and satellite minutia point;and relative angle between a reference angle and an angle of any of theplanet minutia point and satellite minutia point, or any combination ofthese.
 4. The method according to claim 1, wherein the calculation ofthe score further comprises calculating a tension parameter of thesupercluster and basing the score on the calculated tension parameter.5. The method according to claim 1, wherein the calculation of the scorefurther comprises calculating an area of the supercluster and basing thescore on the calculated area.
 6. The method according to claim 1,wherein the calculation of the score further comprises calculating amean number of minutia points in the sets and basing the score on thecalculated mean number of minutia points.
 7. The method according toclaim 1, wherein the calculation of the score further comprisescalculating the number of minutia points in the supercluster and basingthe score on the calculated number of minutia.
 8. The method accordingto claim 1, wherein the initial planet is selected close to a centre ofthe fingerprint reading.
 9. The method according to claim 1, wherein theinitial planet is selected such that a first cluster comprises as manymatching pairs as possible, wherein the method further comprisesrepeating the first iteration with another planet if a poor match isgiven for a previous selected initial planet.
 10. A biometric matchingapparatus comprising a receiver for receiving a first set of minutiapoints of a fingerprint reading; a memory access circuit arranged toaccess a memory holding at least a second set of minutia points of afingerprint template; and a processing device connected to the receiverand the memory access circuit, and arranged to determine whether thefirst set of minutia points match the second set of minutia points byfor a first minutia point in respective set, being assigned as a planetminutia point a) determine pairs including the planet minutia point anda satellite minutia point, respectively, such that a cluster is formedaround the first minutia point in the respective set with the satelliteminutia points; b) compare the clusters of the respective sets whichhave matching features of the pairs between the sets and excludingnon-matching satellites; c) count links in the cluster formed byremaining pairs of the planet minutia point and the satellite minutiapoints; and d) for remaining satellite minutia points, perform a) to c)with respective satellite minutia point assigned as planet minutia pointto form a supercluster by iteration of steps a) to d) and superadditionof the clusters of each iteration wherein link count is stored such thatan aggregate link count is available after the iteration such that theaggregate link count is achieved as the supercluster is built; calculatea score of the supercluster based on the aggregate counted links; andcompare the score with a threshold, wherein the respective fingerprintreading and template are considered to emanate from fingers which areidem if the score reaches the threshold, such that an output indicatingwhether the fingerprint reading and template match is provided.
 11. Theapparatus according to claim 10, wherein the matching features of thepairs comprises a set of parameters including any of distance betweenplanet minutia point and satellite minutia point; relative angle betweenplanet minutia point and satellite minutia point; and relative anglebetween a reference angle and an angle of any of the planet minutiapoint and satellite minutia point, or any combination of these.
 12. Theapparatus according to claim 10, wherein for the calculation of thescore, the processing device is further arranged to calculate a tensionparameter of the supercluster and base the score on the calculatedtension parameter.
 13. The apparatus according to claim 10, wherein forthe calculation of the score, the processing device is further arrangedto calculate an area of the supercluster and base the score on thecalculated area.
 14. The apparatus according to claim 10, wherein forthe calculation of the score, the processing device is further arrangedto calculate a mean number of minutia points in the sets and base thescore on the calculated mean number of minutia points.
 15. The apparatusaccording to claim 10, wherein for the calculation of the score, theprocessing device is further arranged to calculate the number of minutiapoints in the supercluster and base the score on the calculated numberof minutia.
 16. The apparatus according to claim 10, wherein the initialplanet is selected close to a centre of the fingerprint reading.
 17. Theapparatus according to claim 10, wherein the initial planet is selectedsuch that a first cluster comprises as many matching pairs as possible,wherein the processing device is arranged to repeat the first iterationwith another planet if a poor match is given for a previous selectedinitial planet.
 18. A portable data carrier comprising a memory holdinga template of a fingerprint represented by a set of minutia points of areference fingerprint; a matching apparatus according to claim 10,wherein the memory access means is connected to the memory, arranged todetermine if the first set of minutia points and the set of minutiapoints of a reference fingerprint emanates from idem finger; and asecurity mechanism arranged to be unlocked upon the output indicatingthat the fingerprint reading and template match.
 19. A data processingunit comprising a matching apparatus according to claim 10, wherein theaccessed memory is a database comprising a plurality of templates for aplurality of fingers, respectively, arranged to determine, from acalculated score for respective of the templates, which of templatesthat resembles the fingerprint to be checked the most.
 20. The dataprocessing unit according to claim 19, further being arranged todetermine if the fingerprint to be checked and the most resembling oneof the at least one template emanates from fingers which are idem bycomparing the score of the most resembling one of the at least onetemplate with a threshold.
 21. A non-transitory computer readable mediumstoring a computer program comprising computer executable instructions,which instructions cause a computer to, when downloaded to and executedon a processor of the computer, perform the method according to claim 1.